# How do you solve a²-a-1=0 by completing the square?

$a = \frac{1}{2} + \frac{\sqrt{5}}{2} \mathmr{and} a = \frac{1}{2} - \frac{\sqrt{5}}{2}$
${a}^{2} - a - 1 = 0 \mathmr{and} {a}^{2} - a - {\left(\frac{1}{2}\right)}^{2} - \frac{5}{4} = 0 \mathmr{and} {\left(a - \frac{1}{2}\right)}^{2} - \frac{5}{4} = 0 \mathmr{and} {\left(a - \frac{1}{2}\right)}^{2} = \frac{5}{4}$
$\therefore a - \frac{1}{2} = \frac{\sqrt{5}}{2} \mathmr{and} a - \frac{1}{2} = - \frac{\sqrt{5}}{2} \therefore a = \frac{1}{2} + \frac{\sqrt{5}}{2} \mathmr{and} a = \frac{1}{2} - \frac{\sqrt{5}}{2}$